Field of play means batter and on deck batter won't need to have one on.
I would think WARM UP falls under PRACTICE. Because that is what you are doing. Masks are not required during practice. The whole reason they say you don't need one in the field of play is because of the possible breathing/asthma issues and that opens them up to even more negligence if a kid dies of an asthma attack while wearing a mask on the field. Warm up is just as strenuous.
Just guessing, but the thought of having the girls wearing a mask when not on the field is them probably thinking there would be 10+ people crammed in a dugout. You notice there are no number in dugout restrictions? IMO if you allow your kids to spread out in between innings, and maybe sit by their parents, and not in the dugout, they can probably get away with not wearing a mask between innings.
Coaches wearing a mask is going to suck. No lip reading and it will muffle yelling instructions. Not sure I understand no gum chewing? Because they don't want you to share? Choking hazard? Don't want you spitting out a contaminated piece?